August 2024

You’re at MIT now, entering your third year. What are you enjoying most about college?

It's nice. It’s the first stage of adulthood, which isn’t 100% enjoyment. Growing up can be a double-edged sword. Either way, it’s necessary. And with adulthood comes this sort of empowerment to choose what I’m doing to do with the rest of my life.

I certainly have a lot more independence than when I was younger. I was homeschooled and an only child, and with the whole pandemic, I didn’t see many people. I’m glad I was homeschooled, but it’s definitely nice to have more socialization. It’s nice to be in the city. I like Boston. Even though I’m from Texas and lived there my whole life before coming to college, my mother is from Rhode Island and Connecticut, so I have a little bit of the heart of a northeasterner, to some extent. 

What are you studying?

I am a math major. I also recently declared a second major in physics. 

Speaking of physics, you did an award-winning project a couple of years ago on the topological entropy of braids. Can you tell me a little bit about it?

Sure. So, in math, there are objects called braids, which you could think of as hair or thread or whatever, but in an abstract sense, they’re just sort of strings, and they cross over each other. And one interesting thing about braids is how you can relate them to mixing fluids. Say you have some stirring rods and a vat of something viscous like caramel candy, and you want to make sure it mixes around pretty well. You can quantify how well it mixes with topological entropy. If you just sort of spin it in a circle, you haven’t really created much of any disorder at all, so the topological entropy is zero. But if you mix it up well, the entropy is positive. My project illuminates the structure of the braid group to ask: how much do these simple braids mix fluid? 

What first got you interested in braids? 

Well, this was actually part of a research program at MIT called MIT Primes, where high school students get paired with mentors. My mentor suggested some ideas he had in mind for a project about braids, and we worked together over a period of months. He was an excellent mentor. He really knew his stuff and knew how to help guide me through the process. 

You’ve been doing competitive math for a long time and have had a lot of success with it. What has best prepared you for success in competitions like this? 

Good question. I don’t completely understand it myself. In my own case, I think spending a lot of time thinking about mathematics will make you better at math. Even when it wasn’t for an assignment, I was thinking about math. It was something I chose to do and wanted to be doing. Another thing is probably some element of what could be called talent, and I also think there’s probably some element of a positive feedback loop. I was good at it, and being good at math made me glad to think about it more. I heard this quote once that said, “It’s hard to do a really good job on anything you don’t think about in the shower.” When there’s this thing that is always in the back of your mind, that can be a recipe to being next-level good at something. 

Another thing that was useful was when I was younger, I went to the math circle at the University of Texas at Arlington. I got a lot of practice in problem solving and explaining solutions, which was a helpful foundation for doing Math Olympiads in the future, where you have to write up proofs. Plus, I had good mentors. The professor who ran the math circle helped me be able to sit in on other classes, and someone else in the circle noticed my abilities even before the professor did. Then as I got older, I ended up helping run it.

That’s great. I like that idea of being motivated by curiosity and interest, and not just doing math because you want to win.  

Yeah. I think if you do that, even if you do win, it will be a chore. And I certainly did want to win. I enjoy winning. Who doesn’t? But it’s not like I have to win. It’s just that math is something I think about anyway, so I might as well try to level up and keep going. 

There was also the extra incentive of wanting to prove myself, if I wanted to get into top-tier colleges. As a homeschooler, there aren’t a lot of necessarily good ways to do that. It wasn’t a primary reason, but it was a factor. All the factors pointed in the same direction.

What do you find special about competitive math as opposed to solving math problems in a non-competitive setting?

Competing is fun, and it’s a clear goal. Obviously, there’s a wide range of views on this and speed math isn’t for everyone, even if you enjoy math. In the Countdown Round, you have 45 seconds to solve a problem. In an Olympiad, maybe you have like an hour and a half. With research, you might have months. Andrew Wiles famously worked on Fermat’s Last Theorem for seven years. 

But it’s all math, and for me it was fun. I enjoyed it.

I’m interested in this idea of some work not having as many direct applications. I think it’s common for students to question why they’re learning what they’re learning, especially as math concepts become more abstract. How would you explain to a student the value of math without all of its potential real-world applications?

It’s sort of a multiple-sided question. One on hand, math is interesting for its own sake. It’s such a big subject, you could just spend your whole life learning. When I was younger, this is what I thought I was going to do with my life. I didn’t care about applications at all. But I’ve actually started to move away from that. I want to use my math abilities to try and do something in the world that helps people.

But this itself is also an argument for why you should care about math, because not only does it have this beautiful universe of interesting things, it also somehow works in real life, too. There’s a famous phrase: the “unreasonable effectiveness of mathematics.” Why does math, even pure abstract math, also work in the real world? It applies in so many places you might never suspect. Math has a beautiful side and a useful side, and in any case, it teaches you how to think. It’s all gravy.

If you’re in middle school, do math because it’s fun, or do physics or chemistry because it’s fun. The other thing that can be said about math, because it’s underlying other things, you can sort of pivot from math to other subjects. Computer science, economics, you name it.

I’d like to talk a bit about your experience in MATHCOUNTS. Because you were homeschooled, you competed individually at chapter and state competitions, but you got to compete with a team at nationals. What was that like?

It was nice. My first year in 6^th grade, I really vibed with the team. It was nice to have other people my own age to have a good time with and work toward a goal. Some of the people who I did MATHCOUNTS with back in the day, I would go on to continue knowing. People from other state teams I would go on to see at other math contests in high school, and I’m still in touch with some of my teammates.

So it was nice socially, and also nice to get to travel. I think the National Competition was the first time that I did any math contest outside of Texas. Plus, it was really cool after I won in 7^th and 8^th grade to go to New York to be on Kelly and Ryan. 

Do you have any advice for middle school Mathletes or students in general?

Related to math, I used to be on a podcast with a few other people called The Curious Cube, which was sort of a math contest advice podcast. Most of my advice is probably on there, if you want to watch back old episodes. But in a nutshell, I’d say don’t stress out about math contests. If you don’t do well in a contest, plenty of other things will happen in your life. It’s not over in middle school. It’s not over in high school. There will be plenty of other opportunities in the future, so don’t feel like it’s all over. 

Second, don’t feel like if you do badly at a contest that it means you’re bad at math. This ties into what I was saying about speed math earlier—it’s fun and cool, but it’s not necessarily for everyone. Not everyone is going to be super fast at doing mental arithmetic, but that’s okay because there’s so much more to math than doing things quickly. 

Third, how you perform in a contest is not a reflection of you as a person. Your score doesn’t equate to who you are, so don’t attach too much value to it. Don’t let it get you down. Try not to make contests your whole life. Have other hobbies, have things you do for fun. You only get one childhood, so be sure to have fun with it.

Speaking of hobbies, I’d love to hear about your interests outside of school. What are some of your favorite things to do besides math?  

I do acapella here at MIT. I’ve done various forms of singing throughout my life. I used to be in the choir at my church, and my parents are very musical people. I decided to audition for an acapella group called the Chorallaries. It’s “corollary” like a theorem, but spelled “choral” like in choral music…lots of acapella groups have pun names. So that’s been really cool. When I listen to pop music these days, I start thinking about how it would be arranged as an acapella song. It’s nice to have an artistic outlet. I guess this is my example in practice of what I meant about having other things besides just math. 

What’s next for you? What kind of research are you doing, or is there anything else on the horizon that you’re excited about?

These days, something I think about a lot is quantum computing. I took classes in quantum physics and quantum computing and thought it was pretty cool stuff. There’s a lot of appeal to the field, both because it’s interesting math and it has the possibility of having some real-world application. Also, it’s a pretty new field. Shor’s Algorithm is only about 30 years old, compared to something like number theory, which has been around since the ancient Greeks. So yeah, quantum computing is what I think about more these days, but I’m still figuring things out. Part of me thinks that maybe with the way AI is going, maybe I should drop everything else and try to work on AI. Maybe I’ll end up in some other area of math. Maybe I’ll found a startup. Who knows?